Annabella is an elaborated form of Anna — which itself derives from the Hebrew Hannah meaning "grace" — with the Italian bella (beautiful) fused onto the end. The result is a name that means something close to "graceful beauty," which is either accurate or aspirational depending on the specific pet involved. It skews female and reads as operatic in the best possible way.
The Double-Grace Aesthetic
Annabella is a name that suggests a certain kind of dog: long-coated, elegant-moving, possibly wearing a bandana that matches the owner's outfit. Cavalier King Charles spaniels and similar aristocratic toy breeds suit the name's flowing syllables with obvious appropriateness. The name also works for cats whose coloring and bearing justify the operatic register.
The Human Name Crossover
Annabella is a genuine human given name — it appears in SSA records and has historical usage going back to Renaissance Italy. The human name Annabella adds to the pet version's dignity; this is not a name invented for animals. It reads as a full proper name applied with the same care one would give a child's name.
The Counter-Reading
Five syllables (an-na-BEL-la) is genuinely too many for a working recall name — the natural shortening is Bella, which is already one of the most common pet names in North America. Owners who choose Annabella should be prepared to use Bella in practice, which raises the question of whether the full form is worth registering. See also Bella and Anna for the individual components.